Cook failed to survive the first over for the second successive game, but a first win in two months in Australia was a welcome result.

England's bowlers made short work of the composite side - which included five players with Australia experience - to comfortably defend 264 for eight in stiflingly hot conditions and in front of Australia Prime Minister Tony Abbott.

After Boyd Rankin and Chris Jordan made immediate inroads, Ravi Bopara returned four wickets for three runs as the home side were bowled out for 92.

England's innings had been pieced together, on a slow Manuka Oval outfield, thanks to two half-century stands.

Michael Carberry (47) and Gary Ballance (56) added 75 after the early exits of Cook and Joe Root, before an 80-run combination between Jos Buttler (61) and Tim Bresnan (36) rescued matters from 149 for six.

Carberry's innings did his hopes of a recall for the second one-day international plenty of good, especially after Joe Root's own fallow period continued.

Like Cook, the young Yorkshireman managed only one, from 14 balls, before succumbing to former Australia quick Brett Lee's fiery initial burst.

The 37-year-old PM's XI captain reminded England of his best days from the outset as he saw a strong shout for a caught behind off Carberry turned down, before enticing a nervous prod from Cook to a short ball that wicketkeeper Peter Handscomb held.

It was just the skipper's second ball of the day and his recent record now reads one, four, seven and seven from four innings.

Root was then on the end of a rough lbw decision playing back in his crease to Lee.

They were, however, the worst moments on a much-needed good day for England as they won for the first time since their only other win on tour, against a Cricket Australia Invitational XI in Sydney.

While overcoming Australia still remains on the to-do list, Cook's men will at least take positive thoughts to Brisbane for Friday's second ODI.

The team selection reflected an intent to end their losing run after naming a near full-strength XI, with Carberry and James Tredwell the two changes from Sunday's six-wicket defeat to Australia in the opening ODI.

Ian Bell and Ben Stokes were rested while there was also again no room for Steven Finn, to further emphasise how he has regressed on tour.

Carberry pressed his claim to replace Root at the Gabba with a fluent 47 from 50 balls, most pointedly taking the attack to the home bowling once Lee opted for a rest.

He survived a dropped chance on 10, top-edging a pull off Lee, but when he made the same mistake against Ben Cutting trying to reach his half-century it was Lee who held on at mid-on.

Eoin Morgan and Bopara fell cheaply to leg-spinner James Muirhead (three for 52), the former bowled leg stump through the gate.

Ballance confidently reached his second successive half-century, but tired thereafter in the heat and became the leg-spinner's third victim to leave England 149 for six in the 30th over.

Buttler was then lucky not to go first ball, playing back to a Muirhead delivery that skidded into his pads, but with Bresnan he made the most of the reprieve to take a rare chance to build an innings in England colours.

The wicketkeeper-batsman turned the strike over and worked the ball into the wide expanses of the slow outfield - hitting just four boundaries on the way to reaching a run-a-ball half-century.

Bresnan ably complied with Buttler's tactics as they forged a partnership that ensured England's bowlers had plenty to defend.

A home line-up short on batting needed their top-order to fire, but crashed to 24 for three.

Jordan removed Handscomb, when he played on, before Rankin had Luke Pomersbach and Ben McDermott caught behind the wicket.

Veteran Brad Hodge was the last recognised batsmen but after a brisk 28 picked out Carberry on the mid-wicket rope off Tredwell.

That sparked a collapse of five for 19, with Bopara cashing in on the brittle batting, before Lee provided some late entertainment for the home fans.

He smashed Rankin into the Don Bradman Stand over square leg, but Bopara stopped his fun by locating the veteran's off stump and ending England's two-month wait for a win.